一类具非局部源的退化反应扩散方程的爆破性质

数学季刊 ›› 2010, Vol. 25 ›› Issue (3): 352-359.

一类具非局部源的退化反应扩散方程的爆破性质

1. College of Science, Information Engineering University2. China Research Institute of Radiowave Propagation

收稿日期:2005-06-15 出版日期:2010-09-30 发布日期:2023-05-24
作者简介: CUI Guo-zhong(1966- ), male, native of Lankao, Henan, a professor of Information Engineering University, Ph.D., engages in partial differential equation; GAO Yan-ling(1978- ), female, native of Puyang, Henan, a lecturer of Research Institute of Radiowave Propagation, M.S.D., engages in partial differential equation; GUO Cong-zhou(1980- ), male, native of Xihua, Henan, a lecturer of Information Engineering University, M.S.D., engages in partial differential equation.
基金资助:
Supported by the National Natural Science Foundation of China(10571024)；

Blow-up for a Class of Degenerate Reaction-diffusion Equation with Nonlocal Source

1. College of Science, Information Engineering University2. China Research Institute of Radiowave Propagation

Received:2005-06-15 Online:2010-09-30 Published:2023-05-24
About author: CUI Guo-zhong(1966- ), male, native of Lankao, Henan, a professor of Information Engineering University, Ph.D., engages in partial differential equation; GAO Yan-ling(1978- ), female, native of Puyang, Henan, a lecturer of Research Institute of Radiowave Propagation, M.S.D., engages in partial differential equation; GUO Cong-zhou(1980- ), male, native of Xihua, Henan, a lecturer of Information Engineering University, M.S.D., engages in partial differential equation.
Supported by:
Supported by the National Natural Science Foundation of China(10571024)；

摘要/Abstract

摘要： This paper deals with the properties of the solution to a class of nonlocal degenerate reaction-diffusion equation with nonlocal source, subject to the null Dirichlet boundary condition. We first give sufficient conditions for that the solution exists globally or blows up in the finite time. Then the blow-up time is also given. At last, we obtain a property differing from the local source which the blow-up set is the entire interval.

关键词: degenerate reaction-diffusion equation, nonlocal source, global existence, blow-up time, blow-up set

Abstract: This paper deals with the properties of the solution to a class of nonlocal degenerate reaction-diffusion equation with nonlocal source, subject to the null Dirichlet boundary condition. We first give sufficient conditions for that the solution exists globally or blows up in the finite time. Then the blow-up time is also given. At last, we obtain a property differing from the local source which the blow-up set is the entire interval.

Key words: degenerate reaction-diffusion equation, nonlocal source, global existence, blow-up time, blow-up set

中图分类号:

O175.26

崔国忠, 高艳玲, 郭从洲. 一类具非局部源的退化反应扩散方程的爆破性质[J]. 数学季刊, 2010, 25(3): 352-359.

CUI Guo-zhong, GAO Yan-ling, GUO Cong-zhou. Blow-up for a Class of Degenerate Reaction-diffusion Equation with Nonlocal Source [J]. Chinese Quarterly Journal of Mathematics, 2010, 25(3): 352-359.

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